Magnetic Resonance Imaging (MRI) has revolutionized radiological imaging of the internal structures of the human body. It has the advantage of being noninvasive and offers no known health hazards. A variety of MRI protocols are currently available, however image acquisition techniques often suffer from low signal-to-noise ratio (SNR) and/or contrast-to-noise ratio (CNR). Although many acquisition techniques are available to minimize these, post acquisition filtering is a major off-line image processing technique commonly used to improve the SNR and CNR. A major drawback of filtering is that it often diffuses/blurs important structures along with noise.
Two- and higher-dimensional images are currently available through sensing devices that operate on a wide range of frequency in the electromagnetic spectrum—from ultrasound to visible light to X- and γ-rays (Chu et al., Foundation of Medical Imaging, John Wiley Sons, Inc., New York, N.Y., 1993). The usefulness of any of these modalities depends on the perceptability of certain features in the created images. Acquired images are often degraded by various types of artifacts resulting in a lowering of signal-to-noise ratio (SNR) and contrast-to-noise ratio (CNR). Despite high adaptivity and robustness of the human visual perceptual system, low SNR and CNR often degrade the information contained in the image and its utility. Further, image artifacts affect many image processing tasks such as segmentation (Sahoo et al., Computer Vision Graphics and Image Processing 41:233-260 (1988); Udupa et al., Graphical Models and Image Processing 58(3):246-261 (1996)), registration (Wells et al., Medical Image Analysis 1:35-51 (1996); J. Maintz et al., Medical Image Analysis 1:151-161 (1996)), and visual rendition (Udupa, Radiographics 19:783-806 (1999); Höhne et al., (eds.), 3D Imaging in Medicine: Algorithms, Systems, Applications, Springer-Verlag, Berlin, 1990), which are crucial in many applications. Therefore, noise reduction, that is, the improvement of SNR and CNR, is of considerable interest in many imaging applications.
There are basically two approaches for improving SNR and CNR: by changing the method of image acquisition and by utilizing post-acquisition image processing. Improving the method of acquisition usually entails lengthening the acquisition time, or sacrificing spatial resolution, or upgrading of the imaging device hardware. Filtering is an off-line image processing approach, which, if properly designed, may be less expensive than, and as effective as, acquisition improvement approaches without having to sacrifice spatial resolution.
The aim of filtering is to enhance wanted (structure) information and to suppress unwanted (noise) information. Filtering operations may be classified into two categories—enhancing (also know as high pass filtering), wherein wanted information is enhanced hopefully without affecting unwanted information, and suppressing (also known as low-pass filtering), wherein unwanted information is suppressed hopefully without affecting wanted information.
Noise reducing filtering operations may be classified into two major categories. The first is space-invariant filtering (Rosenfeld and Kak, Digital Picture Processing, Academic Press, Inc., Orlando, Fla., 1982), wherein a spatially independent fixed smoothing operation is performed over the entire image. The other is space-variant filtering (Lee, IEEE Transactions on Pattern Analysis and Machine Analysis 2:165-168 (1980)), wherein the smoothing operation is modified by local image features.
A major drawback of space-invariant filtering techniques is that, along with noise, they often blur important structures. To overcome this problem, a variety of local image feature-dependent adaptive filtering strategies have been developed, including local image-statistics-driven filtering (Lee, 1980), least-squares error filtering (Chan and Lim, IEEE Transactions on Acoustic, Speech, and Signal Processing 33:117-126 (1985)), gradient inverse-weighted filtering (Wang et al., Computer Graphics and Image Processing 15:167-181 (1981); Wang, IEEE Transactions on Signal Processing 40:482-484 (1992)), multiple model Kalman filtering (Woods et al., IEEE Transactions on Pattern Analysis and Machine Analysis 9:245-253 (1987)), adaptive recursive filtering using local image features (Rank et al., IEEE Transactions on Image Processing 1:431-436 (1992)), local shape-based template-matched adaptive filtering (Ahn et al., IEEE Transactions on Medical Imaging 18:549-556 (1999)), and gradient-controlled anisotropic diffusive filtering (Perona et al., IEEE Trans-actions on Pattern Analysis and Machine Analysis, 12:629-639 (1990)). This later method has become quite popular, and has been further extended and utilized (Gerig et al., IEEE Transactions on Medical Imaging 11:221-232 (1992); Jackson et al., J. Computer Assisted Tomography 17:200-205 (1993); Bajla et al., Proc. MEDINFO, Part 1:683-686 (1995); Parker et al., Proc. International Society of Magnetic Resonance in Medicine 7:175(1999)) in a variety of applications.
Anisotropic diffusive filtering (Perona et al., 1990) provides a method, in which in each iteration, intensity diffusion takes place between every two spatially close image spatial elements (‘spels’). The magnitude of the diffusion between the two spels is determined by the magnitude of the gradient of image intensity between them. It varies in a monotonically, non-decreasing manner up to a certain gradient magnitude value, and subsequently changes in a monotonically, non-increasing fashion. The flow across boundaries is thus significantly reduced by utilizing information about the presence of boundaries provided by intensity gradients.
A significant drawback of this very useful approach, however, is that it does not offer any image-dependent guidance for selecting the optimum gradient magnitude. More importantly, since it does not use any morphological or structural information to control the extent of diffusion in different regions, fine structures often disappear and fuzzy boundaries are further blurred upon filtering.
Thus, until the present invention, there has remained a need in the art for a reliable method for filtering SNR and CNR in an MRI acquired image in which intensity gradients are accurately determined, but in which selection of the optimum gradient magnitude is permitted and fine structures are detected. To overcome the problems of diffusive filtering in the prior art, the inventors have explicitly utilized ‘object size’ information—or ‘scale’—to control the degree of smoothing that is done in different regions of the image. The notion of scale, as defined herein, is different from the term ‘scale’ used in scale-space computer vision literature (Lindeberg, Scale-Space Theory in Computer Vision, Boston, Mass.: Kluwer, 1994; Lifshitz et al., IEEE Transactions on Pattern Analysis and Machine Intelligence 12(6):529-5407 (1990); McAuliffe et al., in Proc. Visualization in Biomedical Computing, Lecture Notes in Computer Science, 1131, Springer Verlag, Berlin, 1996, pp. 173-182; Pizer et al., Computer Vision and Image Understanding, 69(1):55-71 (1998)), although the intent is the same, i.e., to tailor the processing to local object size.